Coupled oscillators were believed to exclusively exist in a state of synchrony or disorder until Kuramoto theoretically proved that the two states could coexist, called a chimera state, when portions of the population had a spatial dependent coupling. Recent work has demonstrated the spontaneous emergence of chimera states in an experiment involving mechanical oscillators coupled through a two platform swing. We constructed an experimental apparatus with three platforms that each contains a population of mechanical oscillators in order investigate the effects of a network symmetry on naturally arising chimera states. We considered in more detail the case of 15 metronomes per platform and observed that chimera states emerged as a broad range of parameters, namely, the metronomes' nominal frequency and the coupling strength between the platforms. A scalability study shows that chimera states no longer arise when the population size is reduced to three metronomes per platform. Furthermore, many chimera states are seen in the system when the coupling between platforms is asymmetric.